The number of major earthquakes is given by Poisson Distribution with mean of 0.05 per year. A fund is estabilished to $1000 per major earthquake. The fund charges an annual premium, payable at the start of each year, of 60. The fund has initial balance of 300 before the first premium. Claims are paid immediately when there is a major earthquake. If the fund ever runs out of money, it immediately ceases to exist. Assuming no investment income and no expenses, what is the probability that the fund is still functioning after 30 years?
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
The number of major earthquakes is given by Poisson Distribution with mean of 0.05 per year. A fund is estabilished to $1000 per major earthquake. The fund charges an annual premium, payable at the start of each year, of 60. The fund has initial balance of 300 before the first premium. Claims are paid immediately when there is a major earthquake. If the fund ever runs out of money, it immediately ceases to exist. Assuming no investment income and no expenses, what is the
Step by step
Solved in 3 steps
